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Show that: abs((1,a,a^2),(1,b,b^2),(1,c,...

Show that: `abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)`

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ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. IF for the non singular matrix A,A^2=I then find A^-1

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  2. A is a non singular symmetric matrix, write whether A^-1 is symmetric ...

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  3. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

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  4. Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(...

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  5. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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  6. Prove that: |[1, 1+p, 1+p+q],[2, 3+2p, 1+3p+2p], [3, 6+3p, 1+6p+3q ]|=...

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  7. Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,c...

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  8. IF a,b and c are in AP then find the value of the determinant |{:(x+2,...

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  9. Without expanding evaluate the determinant , |{:(sina,sinbeta,sin(a+d...

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  10. Prove that the determinant |{:(x, sin theta, cos theta),(-sin theta,...

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  11. Using properties of determinants evaluate |{:(0,ab^2,ac^2),(a^2b,0,b...

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  12. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  13. Using properties of determinats show that |{:(a,a+b,a+2b),(a+2b,a,a+b)...

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  14. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  15. Evaluate |{:(1,1,1),(nC1,n+2C1,n+4C1),(nC2,n+2C2,n+4C2):}|

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  16. Find the values of k, if the area of traingle is 4sq units and vertice...

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  17. Show that the points A(a,b+c), B(b,c+a) and C(c,a+b) are collinear.

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  18. IF A=[(1,3,3),(1,4,3),(1,3,4):}] then find |A|

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  19. Find the inverse of the matrixA=[(a,b),(c,(1+bc)/a):}] and show that a...

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  20. If A=[(2,2,1),(-2,1,2),(1,-2,2):}] and B=[(1,3,2),(1,1,1),(2,-3,1):}] ...

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